8/5/2014
1
Session XII
Problem solving: sampling distributions
Interval estimation of
population mean, proportion and variance
Exercise with sampling
distributions
1 2 16 , , observations drawn from a NORMAL population
with both mean and variance 100. Find
i) P(Sum > 1550)
ii) P( sample mean < 100 - 0.5 * sample SD)
iii) P( sample SD > 12)
X X Xâ¦
3
Practice Problem
Gotchya runs an entertainment centre. The following data is
from 27 random selected weeknights about number of paying
patrons. His accountants tell him that they need to have at least
fifty five patrons in order to break even on a weeknight.
The partners want to operate on weeknights if they can be at
least 95 percent certain that they will break even at least half
the time. Should Gotchya continue to stay open on weeknights?
The no. of paying patrons on 27 randomly selected weeknights:
61 57 53 60 64 57 54 58 63
59 50 60 60 57 58 62 63 60
61 54 50 54 61 51 53 62 57 4
Solution to Practice problem
Does the 95% C.I. for Ï stay above 0.5? Where
Ï= proportion of breakeven weeknights (# of customers 55 or more)
n=27 sample proportion p = 19/27=0.7037
(1 ) .7037 .2963Ë. .( ) . .( ) 0.0878 27 27
S E p S E p Ï Ïâ Ã
= â = =
So, the 1-sided 95% C.I. for Ï is = (0.7037 - 1.645 Ã 0.0878 = 0.5591, 1)
Since the 95% CI is above 0.50, the owner can be more 95% certain
that they would break even at least half the time and decide to stay
open on weeknights too.
Sample Size Determination
in
Estimating Mean and proportion
6
Determine n in estimating µ
to a given...